Q. 2 I4.2( 5 Votes )

# Simplify each of the following and express it in the form (a + ib) :(1 + i)3 – (1 – i)3

Given: (1 + i)3 – (1 – i)3 …(i)

We know that,

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(a – b)3 = a3 – 3a2b + 3ab2 – b3

By applying the formulas in eq. (i), we get

(1)3 + 3(1)2(i) + 3(1)(i)2 + (i)3 – [(1)3 – 3(1)2(i) + 3(1)(i)2 – (i)3]

= 1 + 3i + 3i2 + i3 – [1 – 3i + 3i2 – i3]

= 1 + 3i + 3i2 + i3 – 1 + 3i – 3i2 + i3

= 6i + 2i3

= 6i + 2i(i2)

= 6i + 2i(-1) [ i2 = -1]

= 6i – 2i

= 4i

= 0 + 4i Rate this question :

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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics